SOLUTION
In this question, we want to explain the term,
Which expression would be easier to simplify if you used the associativeproperty to change the grouping?A. (50 + 50) + 63B. (§ + 3) + }c. [-14+ (-26)] + 67D. (43 +60) + 40
A
Explanation
Step 1
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis', then the expression that takes to be solved is the easier,it is A or D, due to:
[tex]\begin{gathered} A)(50+50)+63=50+(50+63) \\ (100)+63=163\text{ } \\ D)(43+60)+40=43+(60+40) \\ (103)+40=143 \\ \end{gathered}[/tex]the A has twice the number 50, so it is easier
I hope this helps you
Savana walks 3 1/3 miles to the local park. On her way home, she stops at Randolph’s house after 1 2/3 miles to pick up a book. Write and then evaluate a subtraction expression to find how much farther she must walk to get home.
Given
Savana walks 3 1/3 miles to the local park. On her way home, she stops at Randolph’s house after 1 2/3 miles to pick up a book.
Answer
[tex]\begin{gathered} 3\frac{1}{3}-1\frac{2}{3} \\ \frac{10}{3}-\frac{5}{3} \\ \frac{10-5}{3} \\ \frac{5}{3}=1\frac{2}{3} \end{gathered}[/tex]given f(x)=7x+1 and g(x)=7x+5, find (f-g)(x)
SOLUTION:
Case: Functions
Method:
f(x)=7x+1
g(x)=7x+5
Hence:
(f-g)(x)
= (7x+1) - (7x +5)
= 7x + 1 - 7x - 5
=7x +7x +1 - 5
= -4
Final answer:
(f-g)(x) = -4
A number rounded to the nearest hundred thousand is 400,000. The samenumber rounded to the nearest ten thousand is 350,000. What could be thenumber?
SOLUTION:
Case: Rounding of numbers
Method:
the nearest hundred thousand is 400,000
the nearest ten thousand is 350,000
A possible number is any number between:
350,000 and 354,999.
The least number is 350,000 because it is the smallest number that can be rounded up to 400,000 while 354,999 is the biggest number that can be rounded down to 350,000.
Final answer:
351,000
The floor of Mr. Carson's rectangular Office is 7 yards by 5.5 yards. He is going co carpet the entire floor of the office with carpeting that costs $45 per square yard not including installation, which is $175. Which is the total cost to carpet the office? 4.) $1,125.00
Let y be the number of square yards to carpet. The expression that represents the cost is:
[tex]45y+175[/tex]Now, the total square yards to carpet is:
[tex]7\cdot5.5=38.5[/tex]Using this in the expression we've defined from the start,
[tex]45(38.5)+175=1907.5[/tex]We'll get that the total cost to carpet the office is $1,907.50
Consider the steps to solve the equation below. 5x - 6 - 2 (3-7)=29 Which of these is a correct first step in solving this equation? A. 32 – 13 = 29 B. 5. - 6 - 2x = 29 + 7 C. 52 - 6 - 2x – 14 = 29 D. 5.C - 6 - 2 + 14 = 29
Step 1: Let's solve the equation given, as follows:
5x - 6 - 2 (3- 7) = 29
Solving the parenthesis, we have:
5x - 6 - 6 + 14 = 29
The answer is not correct. Student became unresponsive and has not answered if there is a mistake in the statement of the question.
Impossible to move forward.
Session ended by tutor.
please help ASAP!!!! Which rules can be used to rewrite the expression {3/x^3}^-2 ?
The expression is given as ;
[tex](\frac{3}{x^3})^{-2}[/tex]From the expression , you notice that the rules to use in re-writing the expression are:
i) a negative power
ii) A power to a power
So this can be written as
[tex]\lbrack\frac{(3)}{(x^{-3})}\rbrack^{-2}[/tex]Appy power to power rule by product of the exponents to get;
[tex]\frac{(3)^{-2}}{(x^{-3})^{-2}^{}}[/tex][tex]\frac{3^{-2}}{x^6}[/tex]Answer
D. Negative power and power to a power
Which linear inequality is represented by the graph?○y> ²/x- / /30_y² ²/x + ²/50y≤ ² x + = /20y< ²/2 x= 1/2/20
The correct option is C
Explanation:The inequality that is represented by the given graph is:
[tex]y\leq\frac{2}{3}x+\frac{1}{5}[/tex]This is obtained by finding the slope and y-intercept to be 2/3 and 1/5 respectively. The inequality sign is according to the shading of the graph. A dotted line would mean that the inequality sign is strictly "less than" ( < ).
Find the length of side x in simplest radical form with a rational denominator.60°130°X
We will solve using the law of sines as follows:
[tex]\frac{1}{\sin(30)}=\frac{X}{\sin (60)}[/tex]Now, we solve for X:
[tex]\Rightarrow X=\frac{\sin(60)}{\sin(30)}\Rightarrow X=\sqrt[]{3}[/tex]So, the length of X is sqrt(3).
A number is decreased by 40% to 144. What is the original amount?
the original amount is 240
Explanation:Let the original amount = y
the original number is decreased by 40%:
Decrease = y × 40% = y × 0.40
= 0.4y
when it is decreased by 40%, the result is 144:
original amount - decrease = 144
y - 0.4y = 144
0.6y = 144
divide both sides by 0.6:
[tex]\begin{gathered} \frac{0.6y}{0.6}\text{ = }\frac{144}{0.6} \\ y\text{ = }240 \end{gathered}[/tex]Hence, the original amount is 240
9+4t=12-4t one solution,no solution, infinitely many solutions
Given the equation :
[tex]9+4t=12-4t[/tex]The solution of the given equation will be as following:
Step 1 : combine the like terms
[tex]\begin{gathered} 4t+4t=12-9 \\ 8t=3 \end{gathered}[/tex]Step 2 : Divide both sides by 8
[tex]\begin{gathered} \frac{8t}{8}=\frac{3}{8} \\ \\ t=\frac{3}{8} \end{gathered}[/tex]So, the given equation has one solution
Earth follows an elliptical orbit around theSun. At its nearest point on the orbit, it isabout 147 million kilometers from the Sun.At its farthest point, it is about 152 millionkilometers away. What is the percent change, rounded to the nearest tenth, from its nearest point to its farthest?
ANSWER:
3.4%
STEP-BY-STEP EXPLANATION:
We can calculate the percentage of change knowing the two values to be taken into account, just like this:
[tex]\begin{gathered} p=\frac{b-a}{a}\cdot100 \\ \text{ In this case:} \\ p=\frac{152-147}{147}\cdot100 \\ p=\frac{5}{147}\cdot100=\frac{500}{147} \\ p=\: 3.4\% \end{gathered}[/tex]Which means that the percentage of change is 3.4%
-10=2x-4x how do you simplify this
The given formula is,
[tex]-10=2x-4x[/tex]Now solving for x,
[tex]\begin{gathered} -10=-2x \\ x=\frac{-10}{-2}=5 \end{gathered}[/tex]Explain the difference between an independent event and a dependent event. GIve an example to show the difference between the two.
SOLUTION
Dependent event
A dependent event is an event that relies on another event to happen first. Dependent events in probability are no different from dependent events in real life: If you want to attend a concert, it might depend on whether you get overtime at work; if you want to visit family out of the country next month.
For example;
1. Robbing a bank and going to jail.
2. Not paying your power bill on time and having your power cut off.
2. Boarding a plane first and finding a good seat.
Independent events
An independent event is an event that has no connection to another event’s chances of happening (or not happening).
Independent events in probability are no different from independent events in real life
For example;
1. Owning a dog and growing your own herb garden.
2. Paying off your mortgage early and owning a Chevy Cavalier.
3. Winning the lottery and running out of milk.
There are 19 animals on the farm which contains hens and goats. There are 68 legs in total. How many goats are there on the farm?151085
Explanation:
Let the number of hens be
[tex]=x[/tex]Let the number of goats be
[tex]=y[/tex]The number of animals on the farm is
[tex]=19[/tex]This can be represented in an equation below as
[tex]x+y=19-----(1)[/tex]The number of legs given in the question is
[tex]=68[/tex]Hens have 2 legs
Goats have 4 legs
So the number of legs can be represented in the equation below as
[tex]2x+4y=68-----(2)[/tex]Step 1:
We will solve equations (1) and (2) simultaneously
[tex]\begin{gathered} x+y=19----(1) \\ 2x+4y=68----(2) \end{gathered}[/tex]From equation (1), we will make x the subject of the formula
[tex]\begin{gathered} x+y=19 \\ x=19-y-----(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} 2x+4y=68 \\ 2(19-y)+4y=68 \\ 38-2y+4y=68 \\ 38+2y=68 \\ collect\text{ similar terms, we will have} \\ 2y=68-38 \\ 2y=30 \\ divide\text{ both sides by 2} \\ \frac{2y}{2}=\frac{30}{2} \\ y=15 \end{gathered}[/tex]Hence,
The number of goats on the farm is
[tex]\Rightarrow15[/tex]In circle L with mZKNM== 30°, find the angle measure of minor arc KM.
We know that
From the equation we can solve for arc KM:
[tex]\begin{gathered} \frac{KM}{2}=\angle KNM \\ KM=2\cdot\angle KNM \\ KM=2\cdot30^o \\ KM=60^o \end{gathered}[/tex]Answer: arc KM = 60°Nicole’s paycheck last week was $648. She worked 36 hours that week. How much is Nicole paid for each hour of work?
total paycheck = $648
number of hours = 36
Divide the total paycheck by the number of hours
648/36 = 18
$18 per hour
The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 107 Inches, and a standard deviation of 12 inches. What is the probability that the meanannual precipitation during 36 randomly picked years will be less than 109.8 inches?O 0.4192O 0.9192O 0.5808O 0.0808
The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 107 Inches, and a standard deviation of 12 inches. What is the probability that the mean
annual precipitation during 36 randomly picked years will be less than 109.8 inches?
step 1
Find out the z-score
Z score =(x - μ)/σ
we have
x=109.8 in
μ=107 in
σ=12 in
substitute
z score=(109.8-107)/12
z-score=0.2333
Find out the probability
using the tables of z-score
P=0.5922
therefore
the answer is 0.5808
Please help verify if my answers are correct. So far I have f(-3)=3, g(0)=4, g(f(0))=7, don't know at all for f(g(2)), and g(g(2)) I have 6.5.
Radicals and Exponents Indicate whether the statement is true or false
1.
[tex]\begin{gathered} \sqrt[m]{a^n}=a^{\frac{n}{m}}^{} \\ \text{and} \\ (\sqrt[m]{a})^n=(a^{\frac{1}{m}})^n=a^{\frac{n}{m}} \end{gathered}[/tex]Answer 1: true
2.
[tex]\sqrt[]{-a^3b}\sqrt[]{-ab^3}=\sqrt[]{-a^3b\cdot-ab^3}=\sqrt[]{a^4b^4}=a^2b^2[/tex]Answer 2: true
3.
[tex]\sqrt[]{\frac{3}{5}}\text{ is simplified}[/tex]Answer 3: true
4.
[tex]a^x+b^x\ne(a+b)^x[/tex]Answer 4: false
5.
[tex]\begin{gathered} a\sqrt[3]{x+b}+c=0 \\ subtract\text{ c} \\ a\sqrt[3]{x+b}+c-c=0-c \\ a\sqrt[3]{x+b}=-c \\ \text{divide by a} \\ \frac{a\sqrt[3]{x+b}}{a}=\frac{-c}{a}\text{ } \\ \sqrt[3]{x+b}=-\frac{c}{a}\text{ (isolate }\sqrt[3]{x+b}) \end{gathered}[/tex]Answer 5: true
What is the length of 1 period in the function
SOLUTION
[tex]\begin{gathered} \text{Frequency is given as } \\ f=\frac{2\pi}{T},\text{ where T is the period and f the frequency } \\ \text{here, the frequency is 2} \\ 2=\frac{2\pi}{T} \\ 2T=2\pi \\ T\text{ =}\pi \end{gathered}[/tex]Select the correct answer from each drop-down menu.Consider this system of equations:+y=12 (equation A)y-3x = 6 (equation B)The solution for the system of equations is A.(1118/47, 396/47) B.(33/13, 50/13) C.(99/13, 150/13) D.(8, 12)
Given:
[tex]\begin{gathered} \frac{2}{3}x+\frac{3}{5}y=12----(A) \\ \\ \frac{5}{2}y-3x=6-----(B) \end{gathered}[/tex]Required:
To find the solution of the given equations.
Explanation:
Myltiply equation A with 9/2 we get
[tex]3x+\frac{27}{10}y=54----(C)[/tex]Add equation (C) and (B), we get
[tex]\begin{gathered} \frac{5}{2}y+\frac{27}{10}y+60 \\ \\ (\frac{5}{2}+\frac{27}{10})y=60 \\ \\ (2.5+2.7)y=60 \\ \\ 5.2y=60 \\ \\ y=\frac{60}{5.2} \\ \\ y=11.53 \end{gathered}[/tex]Now put y in equation B, we get
[tex]\begin{gathered} \frac{5}{2}(11.53)-3x=6 \\ \\ 28.825-3x=6 \\ \\ -3x=6-28.825 \\ \\ -3x=-22.825 \\ \\ x=\frac{22.825}{3} \\ \\ x=7.6 \end{gathered}[/tex]Final Answer:
[tex](\frac{99}{13},\frac{150}{13})[/tex]Lainey bought a set of 26 markers for $6. What is the cost of 1 marker?Round answers to the nearest hundredths where necessary.
Answer:
$0.23
Explanation:
[tex]\begin{gathered} \text{Cost of 26 markers =}\$6 \\ \therefore\text{Cost of 1 marker =}\frac{\$6}{26} \\ =\$0.23\text{ (to the nearest hundredth)} \end{gathered}[/tex]Brian borrowed $8000 at a rate of 7.5%, compounded annually. Assuming he makes no payments, how much will he owe after 10 years? Round your answer to the nearest cent.
The formula for the amount A after a rate r compounded annually is applied over the value P for t years is:
[tex]A=P(1+r)^t[/tex]In this problem, we have:
P = 8000
r = 7.5% = 0.075
t = 10
So, using those values in the formula, we obtain:
[tex]\begin{gathered} A=8000(1+0.075)^{10} \\ \\ A=8000(1.075)^{10} \\ \\ A\cong16488.25 \end{gathered}[/tex]Therefore, rounded to the nearest cent, after 10 years he will owe $16,488.25.
5 5 pepper cost $2.25 it is in the table below fill in the rest of the table but no money sign rain 50 Cent
First, find the cost of 1 pepper.
Divide the cost given by the number of peppers:
2.25 / 5 = $0.45 per pepper
Now, multiply the cost per pepper (0.45) by the number of peppers asked in the table:
number of peppers : 1 2 3 4
Cost : 0.45 0.45x2 = 0.9 0.45x 3 = 1.35 1.8
PLAC S(7,-5) K(9, -4) I(8, -7) R(9, -9) T(7,-8) and perform: (1) T(x, y) -> (X-6, y) and label S'KTR'T' (2) Reflect SKIRT over the x-axis and label S"K"I"R"T". Write the rule using the notation. (3) Shift SKIRT 4 units up and 5 units right and label S""K"|""R""T". Write the rule. (4) Write the new coordinates of KV after shifting K"9 units up & 12 left.
You have the following points:
S(7,-5) K(9,-4) I(8,-7) R(9,-9) T(7,-8)
T(x,y) => (x - 6,y)
S => S'(7-6,-5) = S'(1,-5)
K => K'(9-6,-4) = K'(3,-4)
I => I'(8-6,-7) = I'(2,-7)
R => R'(9-6,-9) = R'(3,-9)
T => T'(7-6,-8) = T'(1,-8)
T(x,y) => (x,-y) reflection around x-axis
S' => S''(1,5)
K' => k''(3,4)
I' => I''(2,7)
R' => R''(3,9)
T' => T''(1,8)
T(x,y) => (x+5,y+4)
S'' => S'''(1+5,5+4) = S'''(6,9)
K'' => K'''(3+5,4+4) = K'''(8,8)
I'' => I'''(2+5,7+4) = I'''(7,11)
R'' => R'''(3+5,9+4) = R'''(8,13)
T'' => T'''(1+5,8+4) = T'''(6,12)
T(x,y) => (x -12,y+9)
S''' => S''''(6-12,9+9) = S''''(-6,18)
K''' => K''''(8-12,8+9) = K''''(-4,17)
I''' => I''''(7-12,11+9) = I''''(-5,20)
R''' => R''''(8-12,13+9) = R''''(-4,22)
T''' => T''''(6-12,12+9) = T''''(-6,21)
The previous result are the final points after all transformations.
A graph of the result is as follow:
the points S,K,I,R
Preform the indicated operation and express the answer in simplest radical form
hello
the question here is
[tex]3\sqrt[]{7}(14-4\sqrt[]{56})[/tex]step 1
multiply through the bracket by the coeffiecient
[tex]\begin{gathered} 3\sqrt[]{7}(14-4\sqrt[]{56}) \\ (3\sqrt[]{7}\times14)-(3\sqrt[]{7}\times4\sqrt[]{56}) \\ (14\times3\sqrt[]{7})-3\sqrt[]{7}\times4\sqrt[]{4\times14} \\ (42\sqrt[]{7})-3\sqrt[]{7}\times8\sqrt[]{14} \\ (42\sqrt[]{7})-\lbrack(3\times8)\sqrt[]{7\times14} \\ 42\sqrt[]{7}-24\sqrt[]{98} \end{gathered}[/tex][tex]\begin{gathered} 42\sqrt[]{7}-24\sqrt[]{49\times2} \\ 42\sqrt[]{7}-24\times7\sqrt[]{2} \\ 42\sqrt[]{7}-168\sqrt[]{2} \end{gathered}[/tex]Simplify the following equation(3m/4 -3)+9Show all workA. 3m +28/4B. m+9/4C. 3m+ 24/4D. 8m/4
Given:
[tex](\frac{3m}{4}-3)+9[/tex]Find: simplify the given equation.
Explanation:
[tex]\begin{gathered} (\frac{3m}{4}-3)+9 \\ =(\frac{3m-12}{4})+9 \\ =\frac{3m-12+36}{4} \\ =\frac{3m+24}{4} \end{gathered}[/tex]Final answer: the required answer is
[tex]\frac{3m+24}{4}[/tex]determine the slope of the linex = -8
So,
The slope of a line is defined as:
[tex]\frac{change\text{ in y}}{corresponding\text{ change in x}}[/tex]But the value of x doesn't change in a vertical line, i.e., the change in x is always 0; so the definition of slope would require division by 0 (which is not defined).
Therefore, the slope of the line x=-8 is not defined.
solve a real worldproblem. (1 point each)11. A company's cost, in dollars, of manufacturing x tablot computers can be represented by 20% + 200, Thecompany's predicted revenue of selling x tablet computers is 100 + 30%. Write a polynomial expression thatrepresents the pront of selling x tablets. Simplity as much as possible (profitrovenue - cost)12. If the company selle 100 computers, how much pront will the company make?
Explanation:
11) The function representing the cost of production = 20x + 200
let th cost = C(x)
C(x) = 20x + 200
The function representing revenue from the production = 100 + 30x
let the revenue = R(x)
R(x) = 100 + 30x
The formula for profit = revenue - cost
let profit = P(x)
P(x) = R(x) - C(x)
P(x) = 100 + 30x - (20x + 200)
expanding th parenthesis:
P(x) = 100 + 30x - 20x - 200 = 100 - 200 + 30x - 20x
P(x) = 10x - 100
The polynomial expression that represents the profit of selling x tablets:
P(x) = 10x - 100
12) company sells 100 computers
x = 100
P(x) = 10x - 100
we will substitute for x in the function above:
P(x) = 10(100) - 100 = 1000 - 100
P(x) = 900
The company will make $900 as profit for 100 tablet computers